Abstract
We present a brief description of the design of a diagram- based system that supports the development of thinking about mathematical generalisation. Within the software, the user constructs a dependency graph that explicitly shows the relationships between components of a task. Using this dependency graph, the user manipulates graphical visualisations of component attributes which helps them move from the specific case to the general rule. These visualisations provide the user with an intermediate representation of generality and facilitate movement between the specific details of the task, the appropriate generalisations, verbal descriptions of their understanding and various algebraic representations of the solutions.
Work supported by project MiGen (TLRP e-Learning Phase-II, RES-139-25-0381).
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References
Noss, R., Healy, L., Hoyles, C.: The construction of mathematical meanings: Connecting the visual with the symbolic. Educational Studies in Mathematics 33(2), 203–233 (1997)
Mason, J., Graham, A., Johnston-Wilder, S.: Developing Thinking in Algebra. Paul Chapman Publishing, Boca Raton (2005)
Balacheff, N., Kaput, J.: Computer-based learning environments in mathematics. In: Bishop, A.J., Clements, K., Keitel, C., Kilpatrick, J., Laborde, C. (eds.) International Handbook on Mathematics Education. Kluwer, Dordrecht (1996)
Pearce, D., Mavrikis, M., Geraniou, E., Gutiérrez, S.: Issues in the design of an environment to support the learning of mathematical generalisation. In: Proc. of the European Conference on Technology-Enhanced Learning (2008)
Larkin, J., Simon, H.: Why a diagram is (sometimes) worth ten thousand words. Cognitive Science 11, 65–99 (1987)
Novick, L., Hurley, S., Francis, F.: Evidence for abstract, schematic knowledge of three spatial diagram representations. Memory and Cognition 27, 288–308 (1999)
Küchemann, D.: Algebra. In: Hart, K.M. (ed.) Children’s Understanding of Mathematics, pp. 102–119. Antony Rowe Publishing Services (1981)
Moreno, R., Mayer, R.E.: Visual presentations in multimedia learning: Conditions that overload visual working memory. In: Huijsmans, D.P., Smeulders, A.W.M. (eds.) Visual Information and Information Systems, pp. 793–800. Springer, Heidelberg (1999)
Warren, E., Cooper, T.: The effect of different representations on year 3 to 5 students ability to generalise. ZDM Mathematics Education 40, 23–37 (2008)
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Gutiérrez, S., Pearce, D., Geraniou, E., Mavrikis, M. (2008). Supporting Reasoning and Problem-Solving in Mathematical Generalisation with Dependency Graphs. In: Stapleton, G., Howse, J., Lee, J. (eds) Diagrammatic Representation and Inference. Diagrams 2008. Lecture Notes in Computer Science(), vol 5223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87730-1_40
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DOI: https://doi.org/10.1007/978-3-540-87730-1_40
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87729-5
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